Effects of Strong Correlation and Randomness in the Vicinity of the Mott Transition in the Quasi-One-Dimensional Hubbard Model

TL;DR

This paper investigates how strong electron correlations and randomness influence the Mott transition in quasi-one-dimensional Hubbard models, revealing non-universal behaviors and the potential emergence of a Mott glass state.

Contribution

It introduces a systematic expansion approach to study the Mott transition near the critical point, incorporating effects of disorder and long-range transverse hopping.

Findings

Thermodynamic and transport quantities depend on hole-doping with non-universal exponents.

Disorder leads to Mott's law in dynamical conductivity, suggesting a Mott glass state.

Non-perturbative treatment of correlations using exact 1D Hubbard results.

Abstract

We study the strong correlation effects in the vicinity of the Mott metal-insulator transition using coupled clean or disordered Hubbard chains with a infinitely large coordinate number $D_{\perp}\to\infty$ in the direction perpendicular to the chains and with a long-range transverse hopping. Strong electron correlation effects are treated partially non-perturbatively with the use of the exact results for the 1D Hubbard model. In the case of clean systems, the thermodynamic and transport quantities which characterize the Mott transition from the Fermi liquid state, such as the specific heat coefficient, the Drude weight, and the compressibility, are obtained as functions of hole-doping $\delta=1-n$ ($n$, electron density) by the systematic expansion in terms of the inverse of the transverse hopping range $l_{\perp}$. We find that the $\delta$-dependence of these quantities shows non-universal behaviors with exponents depending on the strength of electron-electron interaction. In the presence of disorder, it is shown that the frequency-dependence of the dynamical conductivity obeys the Mott's law, implying the possibility of {\it Mott glass state} for $\delta \to 0$, provided that there exists a finite range interaction.